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A Pair of Dual Integral Equations Occurring in Diffraction Theory

Published online by Cambridge University Press:  20 January 2009

J. Burlak
J. Burlak
Affiliation:
North Carolina State College, Raleigh, North Carolina, U.S.A. Permanent address:The University, Glasgow, W.2
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Dual integral equations of the form

where f(x) and g(x) are given functions, ψ(x) is unknown, k≧0, μ, v and α are real constants, have applications to diffraction theory and also to dynamical problems in elasticity. The special cases v = −μ, α = 0 and v = μ = 0, 0<α2<1 were treated by Ahiezer (1). More recently, equations equivalent to the above were solved by Peters (2) who adapted a method used earlier by Gordon (3) for treating the (extensively studied) case μ = v, k = 0.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 2 , December 1962 , pp. 179 - 187
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

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